A Branch and Cut Search for the Deterministic Optimization of the Thermal Unit Commitment Problem. Part I: Methodology

This two-paper series proposes a novel deterministic optimization approach for the Unit Commitment problem (UC), more specifically for the Security Constrained Unit Commitment problem (SCUC) addressing thermal generating units. In the first part, a suitable mathematical programming model is presented, which contemplates all the inherent constraints and a single set of binary variables, i.e. the on/off status of each generator at each time period, leading to a convex Mixed Integer Quadratic Programming (MIQP) formulation. This gives rise to a very difficult optimization problem, hard to solve through deterministic approaches for high-dimensional instances. To overcome this challenge, an effective solution methodology based on valid integer cutting planes is proposed, and implemented through a Branch and Cut search for finding the optimal solution. In the second of this twopaper series, the application of the model and proposed approach is illustrated with several examples of different dimensions and characteristics.